Blind defense - tricky situation with pair of kings on ace board

[BrassMonkey]

Villian is TAG. What's the best approach to this turn?

Notes on villian:

-Seems decent
-Checked trips on the turn so that he could go for a river raise
-Will call with [censored] in the BB and make loose peels
-Plays three tables at a time
-Will raise 84s 3-handed
-Bets very aggressively post-flop
-Will pause before betting a monster on the river
-Seems to really like calling raises from the blinds
-Will slow on the turn if he has nothing and you call him on the flop
-Called two bets cold in the BB after a raiser and a three bettor with T9o

PokerStars 10/20 Hold'em (4 handed) Hand History Converter Tool from FlopTurnRiver.com (Format: 2+2 Forums)

Preflop: Hero is BB with 7[img]/images/graemlins/diamond.gif[/img], K[img]/images/graemlins/heart.gif[/img].
<font color="#666666">1 fold</font>, <font color="#CC3333">Button raises</font>, <font color="#666666">1 fold</font>, Hero calls.

Flop: (4.50 SB) K[img]/images/graemlins/diamond.gif[/img], A[img]/images/graemlins/heart.gif[/img], 6[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero checks, <font color="#CC3333">Button bets</font>, Hero calls.

Turn: (3.25 BB) 3[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(2 players)</font>
Hero?